Problem O: LY Find Max GCD

### Problem O: LY Find Max GCD

Time Limit: 2 Sec  Memory Limit: 128 MB
Submit: 76  Solved: 8
[Submit] [Status] [Web Board] [Creator:]

#### Description

If A is a sequence of 2*n integers, its pairing is divide A into n pairs of consecutive elements and taking the sum of each pair.

For example, the pairing of A = { 1,2,3,4 } is the sequence { 1+2, 3+4} = { 3, 7 }.

LY are given a A consisting of 2*n positive integers. You are going to perform the following steps:

• Create a new sequence B that is a permutation of A.
• Find the sequence C that is the pairing of B.
• Compute the greatest common divisor of all elements of C and denote it D.

Find and return the largest possible value of D (over all possible choices of B).

each test at most  10

A length 2*n, n>=1&&n<=15

A[i] >=1 && A[i] <=1e9

2

1 2 3 4

5

#### Sample Input Copy

1
3 8


#### Sample Output Copy

11